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Dimensional Analysis :<

  1. May 13, 2009 #1
    Hi guys, have been reading these forums for a very long time, have always found it very helpful and informative.

    There's this problem which I cant seem to get my head around, it seems very straight forward, but every time I try to do it, I always end up doing it wrong. I would greatly appreciate it if anyone could point me in the right direction.

    The problem is:

    Dimensional analysis showed that the following relation describes the drag force F on an airplane

    [tex]\frac{F}{\rho d^{2}u^{2}}[/tex] = f[tex]\left(\frac{\mu}{\rho l u}\right)[/tex]

    Where u the airplane velocity, l is the characteristic length of the airplane, [tex]\rho[/tex] is the surrounding air density and [tex]\mu[/tex] is the viscosity of the air.
    The drag on an airplane cruising at 390km/h in air at atmospheric pressure and temperature is to be determined from tests on a 1:10 scale model placed in a pressurised wind tunnel. To minimise compressibility effect the air speed in the wind tunnel is also to be 390km/h. Determine the air pressure in the wind tunnel, assuming the air temperature for the model and prototype.

    I've tried separating F on the LHS by introducing a constant in the RHS, but that ends up totally wrong :confused:

    Any help would be greatly appreciated!

    Thanks :)
  2. jcsd
  3. Jun 8, 2009 #2
    The only unknown thing is the function f: one must measure it experimentaly. If you only care about one particular real life problem, then you only need the value of f for that problem: you get this value by one experiment on the model that gives the same argument for f as the real life problem.
  4. Feb 19, 2010 #3
    hey thread what answer did u get fir this question. pliz help me everyone.
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